MonographDOI
Functions of Matrices: Theory and Computation
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TLDR
A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.Abstract:
A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Frechet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.read more
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Journal ArticleDOI
A Singular Value Thresholding Algorithm for Matrix Completion
TL;DR: This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.
Journal ArticleDOI
User-Friendly Tail Bounds for Sums of Random Matrices
TL;DR: This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices and provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid.
Proceedings ArticleDOI
Second-Order Attention Network for Single Image Super-Resolution
TL;DR: Experimental results demonstrate the superiority of the SAN network over state-of-the-art SISR methods in terms of both quantitative metrics and visual quality.
Journal ArticleDOI
Most Tensor Problems Are NP-Hard
TL;DR: In this paper, it was shown that determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm, approximating an eigen value, eigenvector, singular vector, or the spectral norm is NP-hard and computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.
Journal ArticleDOI
CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations
Thomas D. Kühne,Marcella Iannuzzi,Mauro Del Ben,Vladimir V. Rybkin,Patrick Seewald,Frederick Stein,Teodoro Laino,Rustam Z. Khaliullin,Ole Schütt,Florian Schiffmann,Dorothea Golze,Jan Wilhelm,Sergey Chulkov,Mohammad Hossein Bani-Hashemian,Valéry Weber,Urban Borštnik,Mathieu Taillefumier,Alice Shoshana Jakobovits,A. Lazzaro,Hans Pabst,Tiziano Müller,Robert Schade,Manuel Guidon,Samuel Andermatt,Nico Holmberg,Gregory K. Schenter,Anna Hehn,Augustin Bussy,Fabian Belleflamme,Gloria Tabacchi,Andreas Glöß,Michael Lass,Iain Bethune,Christopher J. Mundy,Christian Plessl,Matthew Watkins,Joost VandeVondele,Matthias Krack,Jürg Hutter +38 more
TL;DR: CP2K as discussed by the authors is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems, especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations.
References
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Journal ArticleDOI
Linear model reduction and solution of the algebraic Riccati equation by use of the sign function
TL;DR: The sign function of a square matrix can be defined in terms of a contour integral or as the result of an iterated map as discussed by the authors, which enables a matrix to be decomposed into two components whose spectra lie on opposite sides of the imaginary axis.